Perceptual Mapping/MDS

HELLO FRIENDS..... !!!

Hope u have gone through the earlier blogs and got familiar with the concept of clustering. Let's get some more knowledge on clustering...

First let's us go through our today's session where we discussed about another aspect of perpetual mapping i.e. Attribute mapping. Just to make you aware we in our earlier sessions discussed on overall mapping. In overall mapping we consider a direct rating methodology but in attribute mapping we consider different aspects as in the age, taste preferences and so on. In addition we also referred the new Permap techniques where in we checked the co-relate options considering the mean values for comparison.

Let's learn something more about the Permap aka Perceptual Mapping. PERMAP is an interactive Windows-based MDS program that can make any of the standard types of MDS analysis. In addition, it adds some important features that have to do with error analysis and the investigation of the influence of “data types.” You will probably enjoy your ability to change MDS parameters, dimensionality, objective functions, and so forth, “on the fly” while you observe the affect your changes make on a real-time MDS map.

Multidimensional scaling (MDS) is a set of related statistical techniques often used in information visualization for exploring similarities or dissimilarities in data. MDS is a special case ofordination. An MDS algorithm starts with a matrix of item–item similarities, then assigns a location to each item in N-dimensional space, where N is specified a priori. For sufficiently small N, the resulting locations may be displayed in a graph or 3D Visualisation.

While reading about MDS I also came across different types of MDS:

Classical multidimensional scaling

Also known as Torgerson Scaling or Torgerson–Gower scaling, takes an input matrix giving dissimilarities between pairs of items and outputs a coordinate matrix whose configuration minimizes a loss function called strain.

Metric multidimensional scaling

A superset of classical MDS that generalizes the optimization procedure to a variety of loss functions and input matrices of known distances with weights and so on. A useful loss function in this context is called stress, which is often minimized using a procedure called stress majorization.

Non-metric multidimensional scaling

In contrast to metric MDS, non-metric MDS finds both a non-parametric monotonic relationship between the dissimilarities in the item-item matrix and the Euclidean distances between items, and the location of each item in the low-dimensional space. The relationship is typically found using isotonic regression

Louis Guttman's smallest space analysis (SSA) is an example of a non-metric MDS procedure.

Generalized multidimensional scaling

An extension of metric multidimensional scaling, in which the target space is an arbitrary smooth non-Euclidean space. In case when the dissimilarities are distances on a surface and the target space is another surface, GMDS allows finding the minimum-distortion embedding of one surface into another.

Procedure (Steps)

There are several steps in conducting MDS research:

1. Formulating the problem
2. Obtaining input data
3. Running the MDS statistical program
4. Decide number of dimensions
5. Mapping the results and defining the dimensions
6. Test the results for reliability and validity
7. Report the results comprehensively

In marketing, MDS is a statistical technique for taking the preferences and perceptions of respondents and representing them on a visual grid, called perceptual maps.

Well this is all i want to share today but will keep you posted with updates.

Thank You.